This appendix presents the background information necessary to perform both the standard and the extended QRA and the
uncertainty analysis for subscenarios 1, 3, 13 and 49. If only the standard QRA is the objective, much of the information is not required.
B1 Defining the scenario
The sample calculation is defined by the scenario illustrated in Figures B1, B2 and B3. Figure B1 shows the initial part of the event tree leading to the two final parts, A and B. Part A defines subscenarios 1 to 48 and is shown in Figure B2. Part B, defining subscenarios 49 to 96, has the same general appearance, but differs in terms of when the fire starts, see Figure B3. In the initial part of the event tree, four subscenarios are identified which do not result in any unwanted consequences. In these, the fire may have been suppressed by the staff or will not grow. If these subscenarios occur, no evacuation will be necessary.
Initial fire Time of day Flaming fire Fire suppressed by staff day night yes no no no no yes yes yes No conseq. No conseq. No conseq. No conseq. A B
Figure B1. Initial part of the event tree for fire on the hospital ward.
Help needed Asleep Door to patient room open Detector failure Sprinkler failure much little none much little none much little none much little none much little none much little none much little none much little none yes no yes yes yes no no no no no yes yes yes no 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 much little none much little none much little none much little none much little none much little none much little none much little none yes no yes yes yes no no no no no yes yes yes no 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 A yes no
Help needed Asleep Door to patient room open Detector failure Sprinkler failure much little none much little none much little none much little none much little none much little none much little none much little none yes no yes yes yes no no no no no yes yes yes no 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 much little none much little none much little none much little none much little none much little none much little none much little none yes no yes yes yes no no no no no yes yes yes no 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 B yes no
Figure B3. Continuation of the event tree for night-time conditions.
Each subscenario is defined by an individual limit state function which, considering the variables, reflects the current condition. The definitions of all variables and the derivation of the necessary equations are presented in this appendix.
B2 Initial fire probability
In defining the risk to which patients in a hospital ward is exposed, it is necessary to know the fire occurrence rate, i.e. the probability that a fire will start. The statistics in this area are, unfortunately, rather limited. It is usually possible to predict the number of fires occurring in a town or country each year. Some information is given in Rutstein (1979) which relates the probability of fires occurring to the floor area, in m2, of the building. According to this reference the probability of having a fire in a hospital ward per year can be calculated as
pfire = 0.0007 • A0.75 [B1]
This probability has been derived from reports from fire
departments in the UK. The expression gives an average value of the probability and the deviation can be large. As the number of fires in hospitals is low, the reliability of the expression can be questioned. The value of the exponent has been arbitrarily assumed to be 0.75 due to low incident rate. It is, however, generally
assumed that the probability increases with increasing building area. The probability increase can be assumed to be slower and therefore the exponent may be chosen to be less than one. Using this expression for the hospital ward studied in this thesis gives a probability of a fire event of 0.077 fires per year. The floor area used for this calculation was 35 x 15 m2.
In the BSI Draft for development (1997), the overall probability of a fire event in a hospital is assumed to be 0.3 fires per year. This value is of course highly dependent on the size of the hospital. The probability derived using Eq. [B1] is valid only for a single ward in
a hospital and should be less than the probability of a fire starting at any place in a hospital.
Some preliminary Swedish data concerning fire occurrence rates are available from fire departments in the country. The data have been collected from the rescue reports following an emergency operation handled by the fire departments. Almost all Swedish health care facilities (including hospitals) are equipped with smoke detectors which are connected to the local fire department. This means that if a fire occurs in a hospital, it is very likely that the fire department will be notified of the fire. The fire department rescue reports are therefore a good estimate of the number of actual fires in a hospital.
The data are from 3 Swedish fire departments, located in different parts of the country. The incidents reported are those in which a fire has definitely started, and the false alarms have been removed. The number of reported fires is compared with the number of hospital wards in the area covered by the fire department. The ward has been chosen as the dependent variable as the variation in size between wards is assumed to be low. This is a simplification as there are differences between wards, but the number of fires is small and other dependent variables, such as the number of fires per m2, would not necessarily increase the
reliability in the prediction of fire frequency. The total number of fires reported was 59.
Table B1. Fire frequencies in hospital wards per year in three towns in Sweden (Frantzich, 1996).
Town Fire frequency per year Helsingborg 0.038
Lund 0.078
The initial fire probability, pinitial, has been set at 0.07 fires per
year. The value for the wards in Helsingborg is half that of the others, but still of the same order of magnitude. This difference will be examined in the extended QRA, where pinitial, is treated in
some calculations as a random variable. The variable pinitial will
then be assumed to belong to a uniform distribution [0.04, 0.1] fires per year. On the basis of the statistics from the fire
departments, it is assumed that the probability of a fire occurring at night is 0.33 and during the day, 0.67.
The condition leading to evacuation of the ward, is that a fire is initiated and will continue to grow. This means that a smouldering fire will not lead to evacuation unless it develops into a flaming fire. It is assumed that a smouldering fire is harmless, at least on the time scale considered here. Calculations of the conditions in a room in which there is a smouldering fire have been performed using input parameters from Quintiere et al. (1982).
B3 Building characteristics
The calculations were performed on a hospital ward with fixed dimensions to reduce the number of calculation scenarios. The ward complies with the minimum recommendations for hospital wards set out in the former Swedish Building Code (NR, 1989). These recommendations state that the walking distance to the closest evacuation exit from any point on the ward should not exceed 30 m.
It is always assumed that the fire is located in a room close to one exit preventing it from being used. Figure B4 shows the assumed ward with 11 patient rooms, a TV room and a staff room. The exit to the right leads to a protected lobby which, in the other direction, is connected to a second ward. The patients and the staff are considered to be safe when they have reached the protected lobby.
Corridor
1 2 3 4 5 6 S
7 8 9 10 TV 11
Fire
Exit obstructed by fire and unusable
Protected lobby
Figure B4. Ward layout. TV indicates a TV-room and S the staff room.
All rooms in the ward are 5 x 6 x 3.2 m3 and the corridor is 35 x 3 x 3 m3. All patient rooms are equipped with one window to the outside and a door leading to the corridor. The window is 0.9 x 0.9 m2 and the window sill is located 1.2 m above floor level. It is assumed that the window is initially closed in the fire room and breaks when the fire in the room reaches a certain temperature. The door between the patient room and the corridor is 1.2 x 2.1 m2. It may be open or closed according to the subscenario definition. The door between the corridor and the protected lobby is open only during evacuation. Otherwise it is closed, as it is equipped with a closing device. The door has a height of 2.1 m. The patient rooms are not separate fire compartments, but it is assumed that no smoke can leak directly from one patient room to another. The walls between the patient rooms and the corridor prevent smoke from leaking into the corridor.
The ceiling and walls are covered with gypsum plasterboard and the floor is concrete. These conditions are common for the whole ward.
The ward is equipped with a sprinkler system designed to
Swedish regulation RUS 120:4 (1993). The sprinkler heads activate at a temperature of 68°C and are of quick-response type (RTI value 35 m s⋅ ). The coverage area of each sprinkler head is 20 m2, which means two sprinkler heads per patient room.
The likelihood that a sprinkler system will work and be able to extinguish a fire is assumed to correspond to a probability of operation of 0.96. This value was chosen based on judgement combined with information in Bukowski (1997). This value has been used without any uncertainty.
An automatic fire alarm system is installed in the building. The alarm system is equipped with smoke detectors in every patient room and in common areas. The alarm system is monitored for errors and well maintained. The alarm system does not only indicate the presence of a fire, but gives also an alarm to the staff and patients in the ward. The sounding of the alarm informs the staff that there is a fire in the ward.
The likelihood that the automatic fire detection system will work and be able to detect a fire is assumed to correspond to a
probability of operation of 0.94. This value was chosen based on judgement combined with information in Bukowski (1997). The reliability of this system is considered less well defined than that of the sprinkler system. It has therefore been be subjected to
uncertainty in some of the extended QRA calculations. The probability of operation will then follow a uniform distribution [0.9, 0.98]. The mean probability value will be the same with and without the uncertainty consideration.
B4 Staff and patients
There are 22 patients on the ward, two in each patient room. The physical conditions of the patients may vary according to the subscenario. Three different physical conditions have been used to determine their need for help and their mobility. The number of patients in each of the three categories will depend on whether day
or night is considered, table B2. These proportions, used as branch probabilities in the event tree, are purely arbitrary and may vary between wards.
Table B2. Proportions of patients in various groups according to need for help in evacuation.
Need for help Day Sleeping Day Awake Night Sleeping Night Awake Much help needed 0.7 0.1 0.75 0.1 Little help needed 0.2 0.2 0.15 0.15 No help needed. 0.1 0.7 0.1 0.75 Help is needed to make the patient aware of the situation and to prepare the patient for evacuation. Different patient categories require different amount of time. The time period, tcare, is defined as the time spent by the staff in preparing a patient for movement and the physical movement time to the corridor. The values of
tcare for the six different patient categories are given in Tables B3
and B4.
Rather low values have been chosen for tcare. This implies that patients requiring a great deal of help in preparation and movement have been excluded from this investigation.
The movement time along the corridor to the safe lobby is
determined by tPpatM and includes the time required by the staff to
reach the next patient. In the extended QRA, both tcare and tpatM are
Table B3. Duration of tcare and tpatM for the standard QRA. Values
are in seconds.
Awake or asleep Need for help tcare tpatM
Awake None 10 25 Awake Little 15 40 Awake Much 20 50 Asleep None 13 25 Asleep Little 25 50 Asleep Much 40 60
Table B4. Duration of tcare and tpatM for the extended QRA. Values
are the mean and standard deviation in seconds.
Awake or asleep Need for help tcare tpatM
Awake None [5,5] [20,5] Awake Little [10,5] [30,30] Awake Much [15,5] [40,40] Asleep None [10,3] [20,5] Asleep Little [20,5] [40,30] Asleep Much [30,10] [50,30]
The number of members of staff on the ward depends on if it is daytime or night-time. During the day, 4 nurses are on the ward and during the night 2. There are never more nurses than patients in one room.
After the fire has been detected by either the automatic fire alarm or manually, the staff spend some time reacting and interpreting the situation. As they are trained to respond to various kinds of signals, the response time, trespstaff
, is rather short. The staff response time is assumed to be normally distributed [10,3] seconds in the extended QRA. In the standard QRA, the value is assumed to be 10 seconds.
If a fire occurs, the staff will most likely be able to put it out. Therefore, situations in which the ward must be evacuated have the following characteristics; the staff are not able to distinguish the
fire and it does not self-extinguish. This is a very infrequent event and its probability has been estimated on the basis of statistics and discussions with other fire professionals. The probability of successful extinction by the staff or self-extinguishment, has been set to 0.95.
If the staff do not tackle the fire, they will move towards the patients. This movement time, tstaffM is assumed to follow a normal
distribution [15,5] seconds. In the standard QRA the value used is 20 seconds.
The evacuation of the ward must be completed before untenable conditions arise. The limits used to define untenable conditions are given in Table B5. The condition first reached determines the available time for evacuation. Two levels of untenable conditions have been used in the risk analysis, critical and lethal.
The critical conditions are similar to those recommended for fire safety design in Sweden. In addition to the critical conditions, lethal conditions were used to define the available escape time. The lethal conditions chosen were based on work by Purser (1995) and are assumed to be relevant for hospital environments. The temperature levels have been deliberately chosen to be slightly lower than Purser's suggestion due to the assumed lower lethal limits for hospital patients. He suggested exposure to 120°C for some minutes as the lethal limit assuming water-vapour-saturated smoke.
Table B5. Untenable conditions.
Type Critical Lethal
Radiation at floor level 2.5 kW/m2 2.5 kW/m2
Smoke layer height (z) 1.5 m if Tg > 80°C 1.0 m if Tg > 100°C
Temperature in layer (Tg) 80°C if z<1.5 m 100°C if z < 1.0 m
Toxicity is measured in terms of the Fractional Effective Dose, FED, which considers the effect of a number of toxic gases, Bukowski et al. (1989).
B5 Fire specifications
The energy release rate from the fire is assumed to follow an αft2
relationship. It is assumed that the fire always arises in a patient room and does not spread to a neighbouring room or corridor during the time of interest. The time available for escape depends on how fast the fire grows, i.e. the growth rate of the fire, αf.
It is reasonable to assume a low value of the growth rate. Tests on the fire behaviour of hospital beds, indicate a growth rate of approximately 0.01 kW/s2 (Holmstedt et al., 1983). The bed used for that test was a standard bed used in hospitals until a couple of years ago. Newer beds are especially designed to be difficult to ignite and fires in such beds are reported to have a substantially slower growth rate in initial fire development.
After the fire in the Hillhaven Nursing Home in Norfolk, Virginia, USA in 1989 it was determined that the fire in the bed ignited, had a growth rate of approximately 0.01 kW/s2 (Nelson et al., 1991). In simulations of patient room fires growth rates in the region of 0.0001 - 0.00025 kW/s2 have been used which are very low (Notarianni, 1993).
After examining similar fires it was decided to use a fire growth rate following a lognormal distribution [0.01,0.005] kW/s2. This will result in untenable conditions in the fire room within a few minutes, which is in good agreement with experiments and post- fire investigations. The value used for the standard QRA was chosen to be 0.007 kW/s2 to include the very slow growing fires reported.